Statistics

• Statistics


  A branch of Mathematics that deals with the collection, organization, presentation, analysis, and interpretation of data
• Collection


  Gathering of information or data
• Organization or presentation


  Summarizing data in graphical, tabular or textual forms
• Analysis


  Describing the data using statistical methods and procedures
• Interpretation


  Making conclusions based on the presented data
• Population


  A complete collection of all elements (scores, people...) to be studied
• Census


  A collection of data from every element in a population
• Sample


  A sub-collection of elements drawn from a population
• Types of sample


  • Random sample
  • Convenience sample
  • Stratified random sample
  • Cluster sample
  • Systematic random sample
• Random sample


  Each member of the population has an equally likely chance of being selected. The members of the sample are chosen independently of each other
• Convenience sample


  A type of sample that is chosen so that it will be easy for the researcher
• Stratified random sample


  The population is divided into subgroups, so that each population member is in only one subgroup. Individuals are chosen randomly from each subgroup
• Cluster sample


  A type of sample that consists of items in a group such as neighborhood or a household. The group may be chosen at random
• Systematic random sample


  Obtained using an ordered list of population, thus selecting members systematically from the list
• Examples of Statistics used around us:

  • In education, it is frequently used to describe test results

  • In Science, the data resulting from experiments must be collected and analyzed

  •In government, many kinds of statistical data are collected all the time
• Data


  A collection of facts or set of information or observation under study
• Types of data

  • Quantitative data
  • Qualitative data
• Quantitative data


  Numbers representing counts or measurements, such as weights
• Qualitative data


  Data that can be separated into different categories that are distinguished by some nonnumeric characteristics
• Types of quantitative data

  • Discrete
  • Continuous
• Discrete data


  Result from either a finite number of possible values or countable number of possible values as 0, or 1, or 2, and so on
• Continuous data


  Result from infinitely many possible data that can be associated with points on a continuous scale in such a way that there are no gaps or interruptions
• Levels of measurement

  • Nominal
  • Ordinal
  • Ratio
  • Interval
• Nominal level of measurement


  Data that consist of names, labels, or categories only
• Ordinal level of measurement


  Data that may be arranged in some order but differences between data values either cannot be determined or are meaningless
• Interval level of measurement


  Like the ordinal level, but meaningful amounts of differences between data can be determined. It has no inherent (natural) zero starting Point (where none of the quality is present)
• Ratio level of measurement


  The interval level modified to include the inherent zero starting point (where zero indicates that none of the quality is present)